Question

A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for soccer or volleyball. Out of the total 80 people who liked soccer, 30 also liked volleyball. There were 45 people who liked volleyball.Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points)Like soccer Do not like soccer TotalLike volleyball A D GDo not like volleyball B E HTotal C F IPart B: What percentage of the survey respondents did not like either soccer or volleyball? (3 points)Part C: Do the survey results reveal a greater dislike for soccer or volleyball? Justify your answer. (2 points)

Answer 1

A: 80 like soccer, 20 do not like soccer

45 like volleyball, 55 do not like volleyball

B: 5%

C: Greater dislike for volleyball

Explanation:

There are a total of 100 people in the survey of them, 80 liked soccer, which included the 30 who liked both soccer and volleyball. 45 liked volleyball, which included the 30 who liked soccer and volleyball.

Let A represent the number of students who like soccer

Let B represent the number of students who like volleyball

Let AnB represent the number of students who like both soccer and volleyball.

Then we have

A = 80 - AnB = 80 - 30 = 50

B = 45 - AnB = 45 - 30 = 15

So 50 students just liked soccer. 15 Students just liked volleyball. 30 Students liked both soccer and volleyball. That leaves 5 students who didn't like either soccer or volleyball.

50 (just soccer) + 15 (just volleyball) + 30 (both) + 5 (neither) = 100

Part B: Only 5 out 100 student didn't like soccer or volleyball, so that's 5/100 = 1/20 = 0.05 = 5%

Part C: More students liked soccer than volleyball